Understanding Light Polarization: An Intuitive Explanation

[Spathi]

TL;DR Summary

...This analogy is incorrect, since it is possible to put between two perpendicular polarizers a third one and the intensity will increase:

In this thread, I set out an analogy illustrating what quantum entanglement is; further in my post there is a description of the experiment with polarizers and waveplates, corresponding to this model (CHSH inequalities). To understand it, you need to understand what polarization is. I have read in one book, that quantum mechanics is easier to study starting with optics.

I had two intuitions about what polarization is, both wrong:

1) The light beam is “flat” and has a direction perpendicular to the direction of its movement, i.e. the beam is like a thin long plate, the normal to this plate is perpendicular to the line of motion of the beam, and the direction of this normal is the polarization. When light passes through a polarizer, rays with a certain direction of the normal are absorbed, so light cannot pass through two perpendicular polarizers (only rays with a horizontal normal pass through the first, and only rays with a vertical normal pass through the second).

This analogy is incorrect, since it is possible to put between two perpendicular polarizers a third one and the intensity will increase:



(I write a link with timecode, will it work on this forum?)

2) Then one can then propose the idea that the polarizer rotates the polarization of the light, but obviously this is even more frivolous?

Can you suggest another intuitive model, more adequate?

 

[Drakkith]

Can you suggest another intuitive model, more adequate?

Why not just use the actual model instead of an analogy? The field vectors oscillate perpendicular to each other and to the direction of travel, and the polarizers attenuate some amount of the intensity based upon the angle between the polarizer and the direction of the electric field vector. Whatever is left should oscillate in the same direction as the polarizer. A difference of 45 degrees cuts the light in half, while a 90 degree difference cuts it to zero. Thus, a three-plate polarizer setup, with each plate at an increasing 45 degree difference to the plate in front of it, cuts the light in half twice (ignoring the intensity cut of the first polarizer, if any depending on the initial light polarization), leaving a quarter of the light to get through. One-quarter is, obviously, more than the zero intensity of two polarizers placed at 90 degrees to each other.

2) Then one can then propose the idea that the polarizer rotates the polarization of the light, but obviously this is even more frivolous?

I'm not sure what you mean by 'frivolous', as rotating the polarization of the beam is exactly what happens. A vertically polarized beam of light that passes through a polarizer whose direction of polarization is placed at a 45 degree difference to the light beam will emerge with a polarization equal to that of the polarizer (and a cut in intensity as well). The beam's polarization has been 'rotated'.

The light beam's intensity in a polarization direction is essentially projected onto the direction of the polarizer. The greater the difference in angle between the two, the less there is to project onto the polarizers direction. This type of 'projection', where we take a motion in one or more axes and convert it into a single axis (the axis of the polarizer in this case), is extremely common in science, engineering, and math.

 

[Claude Bile]

Two insights I have personally found helpful;

1. The Jones matrix of a polariser includes "cross-terms". This means that a field component in x can generate a field component in y or vice versa. Polarisers don't simply attenuate the x or y component of the field, the behaviour is much richer than that.

2. A nice thought experiment is to keep adding polarisers. Each polariser (appropriately rotated) increases the transmission. In the continuous limit, you get smooth rotation of the polarisation without loss.

I would echo Drakkith's sentiment; viewing polarisers as being able to rotate the polarisation of an EM wave is not frivolous at all, it's a rather key insight.

 

[vanhees71]

I don't know, what you mean by "polarizer". It depends on what you use. If you have a polaroid foil it's of course lossy, i.e., it let's through light that is linearly polarized in one direction and absorbs the light completely when polarized in the perpendicular direction. Mathematically it acts as a projection operator in the polarization direction it lets through. So they do not simply rotate the polarization direction but absorb a part of the light if not oriented in direction of the incoming light.

 

[Spathi]

I heard that a rope can serve as an analogy for light, then a gap will be an analogy for a polarizer. Linear or circular waves can be sent along the rope; if you pass a rope through a slot, then the circular oscillation will turn into a linear one, and if you put two perpendicular slots, then the wave will not pass. However, if a third slot is placed between these two, at an angle of 45 deg, then the wave will again partially pass. Is that true? I tried to experiment with a rope, but it was not possible to make sufficiently high-quality conditions of the experiment.

 

[Spathi]

I don't know, what you mean by "polarizer". It depends on what you use. If you have a polaroid foil it's of course lossy, i.e., it let's through light that is linearly polarized in one direction and absorbs the light completely when polarized in the perpendicular direction. Mathematically it acts as a projection operator in the polarization direction it lets through. So they do not simply rotate the polarization direction but absorb a part of the light if not oriented in direction of the incoming light.

Maybe you mean that a polarizer and a polarizing beam splitter (PBS) is not the same?

 

[vanhees71]

There are many "polarizers". A polarizing beam splitter is also one example. A polaroid foil is another.

 

[Cthugha]

Mathematically it acts as a projection operator in the polarization direction it lets through. So they do not simply rotate the polarization direction but absorb a part of the light if not oriented in direction of the incoming light.

Nobody doubted that. The point is that we have Malus's law, so that the transmission probability depends nonlinearly on the relative angle between the polarizer and the light field.

The scenario considered by Claude Bile is that you have light oriented along a certain polarization (say, vertical) and you place a polarizer at an angle of 90 degrees to that (so horizontal). No light will pass at all. Now instead of placing one polarizer at an angle of 90 degrees, one may place N polarizers all oriented at 90/N degrees with respect to the last polarizer with the first polarizer oriented at 90/N degrees with respect to the polarization of the light field. Neglecting reflection at surfaces, the total transmitted intensity will increase with N and may become arbitrarily close to unity as N approaches infinity. And this array of polarizers indeed acts as a lossless polarization rotator in the limit of large N.

 

[vanhees71]

That's, of course, true, but also well understood using the projection operators.